We know neutron stars as a very massive object with extremely strong gravitational forces that composes mostly of neutrons.

I couldn't help but wonder, what would happen if an object fell into a neutron star, what would become of it? Will it turn it into neutrons as well? And will be any sort of accompanying radiation emission?

Neutron stars are nowhere near 'composed entirely of neutrons'. There's plenty of electrons in the crust, and most likely an outer envelope of fully ionized iron. So anything hitting that envelope will probably be fully ionized as well, but what fraction of it (if any) is likely to undergo fusion into heavier elements I'm not sure about, especially since it will be ripped apart by tidal forces first.
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Stan LiouFeb 8 '14 at 11:02

@StanLiou Thanks for pointing that out, I will edit the question accordingly.
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YodaFeb 9 '14 at 14:18

@StanLiou: Given that the energy release per unit mass at the moment of impact is much larger than nuclear binding energy per unit mass of the impactor, ionisation and nuclear bonds are irrelevant. The outcome would be the same as if the object would be just a set of protons and neutrons.
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Alexey BobrickFeb 9 '14 at 15:38

1 Answer
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No detailed calculations, but a qualitative answer: Depending on the trajectory of the impactor, the results will vary a bit, but it's clear, that the potential energy of the impactor will be transformed into a high amount of kinetic energy before the impact happens. The kinetic energy will then be transformed mainly into heat during the impact, transforming a substantial part of the mass of the impactor into x-rays and gamma rays.

The remnants of the impactor will be transformed into a plasma, with most of the electrons moving independently of their former nuclei, and dispersed mainly into the atmosphere (a thin layer of a few millimeters) of the neutron star. The energies will be high enough to trigger nuclear fusion as well as fission, together with other high-energy particle reactions. Part of the energy will be transformed into magnetic fields, which can also be very strong on neutron stars.

No much intermixing with the interior of the neutron star is to be expected in the first instant for small impactors due to the high inertia and density of the inner parts of the neutron star.

In some cases the impact could trigger the collapse of the neutron star into a black hole, depending of the mass of the neutron star, and the mass of the impactor.

More on the inner structure of neutron stars on Wikipedia.
("Matter falling onto the surface of a neutron star would be accelerated to tremendous speed by the star's gravity. The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star.")